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HallsofIvy
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HallsofIvy
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Join Date
01-27-2012
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08:41 AM
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Today,
08:28 AM
HallsofIvy
replied to a thread
Asymptotically stable/unstable system of linear D.E.
in
Differential Equations
Find the eigenvalues of the matrix, in terms of "a". The system is "stable" if all eigenvalues are negative, "unstable" if any are positive.
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1 replies | 275 view(s)
Today,
08:26 AM
HallsofIvy
replied to a thread
Equation of Paths for Second order ODE: d^y/dx^2 - x - 2x^3 = 0
in
Differential Equations
The standard method would be to introduce the new variable, u= \frac{dy}{dx}. Then \frac{d^2y}{dx^2}= \frac{du}{dx}= 2x^3+ x. Now you have the...
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4 replies | 417 view(s)
12-08-2018,
10:30 AM
HallsofIvy
replied to a thread
Expected value: Suppose people randomly pick a number between 0 and 1....
in
Probability / Statistics
This is meaningless until you specify a probability distribution.
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13 replies | 592 view(s)
11-26-2018,
08:25 AM
HallsofIvy
replied to a thread
Point of inflection, max and min?
in
Calculus
At a "max" or "min" or "inflection point" of a polynomial the first derivative must be 0. At an inflection point the second derivative is also 0. ...
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7 replies | 236 view(s)
11-26-2018,
07:57 AM
HallsofIvy
replied to a thread
I dont understand vector matrices please help
in
Intermediate/Advanced Algebra
The set, W, as you show it is not a subspace. You must mean the subspace spanned by the matrices \begin{bmatrix}-5 & 0 \\ 0 & -3 \end{bmatrix} and...
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3 replies | 165 view(s)
11-26-2018,
07:45 AM
HallsofIvy
replied to a thread
Finding X when there are two X's
in
Intermediate/Advanced Algebra
What you have is correct. Simplifying a little, think of it as Ax+ Bx= C (A= (W)*(Q)*(D)*(F)*(C), B= (W)*(1-Q)*(P)*(D)*(F)*(C), and c= Output). We...
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3 replies | 157 view(s)
11-23-2018,
08:04 AM
HallsofIvy
replied to a thread
how to solve the equation
in
Beginning Algebra
Since x^2+ y= 7, y= 7- x^2. Then y^2+ x= (7- x^2)^2+ x= x^4- 14x^2+ 49+ x= x^4- 14x^2+ x+ 49= 11. x^4- 14x^2+ x+ 38= 0. Solve that "quartic"...
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3 replies | 405 view(s)
11-22-2018,
09:09 AM
HallsofIvy
replied to a thread
Shading the region implied by a double integration expression
in
Calculus
The outer integral, with constant limits, 0 and 1, is with respect to x so mark x= 0 and x= 1 on the x-axis of an xy coordinate system. For each x...
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2 replies | 272 view(s)
11-22-2018,
08:33 AM
HallsofIvy
replied to a thread
Write an equation for a line passing through the points ( 1 , 6 ) and ( − 2 , 0 )
in
Beginning Algebra
These are not true. y= 6 only for x= 1 not for any other x. Since you have replaced y with 6 you must replace x with 1. Similarly y= 0 only for x=...
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6 replies | 535 view(s)
11-13-2018,
08:11 AM
HallsofIvy
replied to a thread
Laplace's equation: △u =1r∂u∂r+∂2u∂r2+1r2∂2u∂ϕ2
in
Calculus
You could, at the very least, have put "/" to indicate fractions and derivatives: \left(1/r\right)\partial u/\partial r+ \partial^2 u/\partial^2r+...
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1 replies | 329 view(s)
11-12-2018,
09:23 AM
HallsofIvy
replied to a thread
Find smallest integer x>0 that solves congruence: 11x ≡ 6(mod68)
in
Intermediate/Advanced Algebra
11x- 68k= 6 Euclidean algorithm: 11 divides into 68 6 times with remainder 2: 1(68)- 6(11)= 2. 2 divides into 11 5 times with remainder 1:...
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2 replies | 591 view(s)
11-11-2018,
06:50 PM
HallsofIvy
replied to a thread
Equation of Paths for Second order ODE: d^y/dx^2 - x - 2x^3 = 0
in
Differential Equations
Your differential equation is \frac{d^2y}{dx^2}- x- 2x^3= 0 and you are asked to "sketch the paths in the xy-plane"? I would just write the...
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4 replies | 417 view(s)
11-11-2018,
06:42 PM
HallsofIvy
replied to a thread
If I have nine 100 sided dice & need them to land on numbers 1-15, what is...?
in
Probability / Statistics
If each die has 100 sides, and all 100 are equally likely, the probability that a specific die comes up 1-15 is 15/100= 3/20. The probability a...
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4 replies | 355 view(s)
11-09-2018,
08:38 PM
HallsofIvy
replied to a thread
Biased Dice Question: biased so that i lands on 1 one quarter of the time.
in
Probability / Statistics
a dice is biased so that i lands on 1 one quarter of the time. So P(1)= 0.25 So P(3)= 2P(2)= 3P(4) So P(5)= 1.1P(4)= .9P(6). Those must...
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5 replies | 409 view(s)
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